They do contain part of the brain, but I haven't seen any info regarding what areas of the brain, exactly, are located there...For all I know, the lekku contain their taste buds or a radar system.
According to Wookiepedia, a top portion of the lekku contains brain tissue that controls basic motor functions and houses repressed subconscious memories. It notes that force to the top portion of the lekku can incapacitate a Twi'lek or cause brain damage. It also notes that Rianna Saren's right lek was cut off, but this must have been below the actual brain matter as she suffered no brain damage.
Seems like kind of a weird way for evolution to go. Basic motor skills--let's keep them on the outside
where they're more easily damaged!